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Competitive exploration of rectilinear polygons

2006
*
Theoretical Computer Science
*

We prove constant

doi:10.1016/j.tcs.2005.11.032
fatcat:bfuyjcmn45e4fdnxw5eei34nna
*competitive*strategies and lower bounds for*exploring*a simple*rectilinear**polygon*in the L 1 metric. ...*Exploring*a*polygon*with robots when the robots do not have knowledge*of*the surroundings can be viewed as an online problem. ... Conclusions We have presented constant*competitive*strategies and lower bounds to*explore*a*rectilinear*simple*polygon*in the L 1 metric with one or more robots. ...##
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Optimality and competitiveness of exploring polygons by mobile robots

2011
*
Information and Computation
*

For

doi:10.1016/j.ic.2010.09.005
fatcat:ofqgtwbrxjg3fgtbnglm3s7rwa
*competitiveness*the situation is more optimistic: we show a*competitive**exploration*algorithm for*rectilinear**polygons*whenever the sensing area is a square, for both tasks, regardless*of*the metric ... Most*of*our results concern*rectilinear**polygons*. ... For the problem*of**competitiveness**of*on-line*exploration**of**rectilinear**polygons*, our results are less complete: we showed a*competitive*algorithm for a robot with square sensing area, regardless*of*the ...##
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Optimality and Competitiveness of Exploring Polygons by Mobile Robots
[chapter]

2009
*
Lecture Notes in Computer Science
*

For

doi:10.1007/978-3-642-04128-0_23
fatcat:oyvam5vi7vfo5byd7djoxn7ir4
*competitiveness*the situation is more optimistic: we show a*competitive**exploration*algorithm for*rectilinear**polygons*whenever the sensing area is a square, for both tasks, regardless*of*the metric ... Most*of*our results concern*rectilinear**polygons*. ... For the problem*of**competitiveness**of*on-line*exploration**of**rectilinear**polygons*, our results are less complete: we showed a*competitive*algorithm for a robot with square sensing area, regardless*of*the ...##
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Polygon Exploration with Time-Discrete Vision
[article]

2010
*
arXiv
*
pre-print

a matching upper bound by providing an O(log A)-

arXiv:0807.2358v2
fatcat:ej2a5yrhlrg3fernvpoahzlapq
*competitive*strategy for simple*rectilinear**polygons*, using the assumption that each edge*of*the*polygon*has to be fully visible from some scan point. ... , a*competitive*strategy can be achieved only for limited aspect ratio A (the ratio*of*the maximum and minimum edge length*of*the*polygon*), i.e., for a given lower bound on the size*of*an edge; we give ... Difficulties*of*Discrete Vision The main result*of*this paper is to develop an*exploration*strategy for simple*rectilinear**polygons*. ...##
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Online Vertex Exploration Problems in a Simple Polygon

2013
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IEICE transactions on information and systems
*

We also study the case

doi:10.1587/transinf.e96.d.489
fatcat:2gl6k5smpbdqzezpghzbr3s5nu
*of*a*rectilinear*simple*polygon*, and give a 1.167-*competitive*algorithm. ... The information*of*the*polygon*is given online. As the*exploration*proceeds, the searcher gains more information*of*the*polygon*. We give a 1.219-*competitive*algorithm for this problem. ...*Competitive*Analysis for*Rectilinear**Polygon*In this section, we analyze the*competitive*ratio*of*AOE for a*rectilinear**polygon*(see Fig. 11 ). ...##
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Polygon exploration with time-discrete vision

2010
*
Computational geometry
*

a matching upper bound by providing an O (log A)-

doi:10.1016/j.comgeo.2009.06.003
fatcat:agedksm4v5hw5k4aup6s3nmlhu
*competitive*strategy for simple*rectilinear**polygons*, using the assumption that each edge*of*the*polygon*has to be fully visible from some scan point. ... , a*competitive*strategy can be achieved only for limited aspect ratio A (the ratio*of*the maximum and minimum edge length*of*the*polygon*), i.e., for a given lower bound on the size*of*an edge; we give ... Difficulties*of*time-discrete vision The main result*of*this paper is to develop an*exploration*strategy for simple*rectilinear**polygons*. ...##
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Page 2058 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
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Mathematical Reviews
*

The main result

*of*the paper is a*competitive*strategy in the L; metric for*exploring**rectilinear**polygonal*rooms with a bounded number*of**rectilinear**polygonal*obstacles. ... In particular, the authors give a polynomial-time off- line algorithm for*exploring*simple*rectilinear**polygons*in the L, metric. ...##
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Exploring the Outer Boundary of a Simple Polygon

2021
*
IEICE transactions on information and systems
*

We investigate an online problem

doi:10.1587/transinf.2020edp7234
fatcat:vz633deiszfupk2kcsk3inffty
*of*a robot*exploring*the outer boundary*of*an unknown simple*polygon*P. The robot starts from a specified vertex s and walks an*exploration*tour outside P. ... We consider P in two scenarios: convex*polygon*and concave*polygon*. For the first scenario, we prove a lower bound*of*5 and propose a 23.78-*competitive*strategy. ... [11] studied the*exploration**of**rectilinear**polygon*without holes under discrete visibility. They showed an O(logA)-*competitive*strategy, where A is the aspect ratio*of*the*polygon*. Premkumar et al ...##
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Competitive searching in a generalized street

1999
*
Computational geometry
*

We present an on-line strategy for a robot to find the target in an unknown

doi:10.1016/s0925-7721(99)00015-2
fatcat:r7pol4ppbzbg5exo7ujkld6jfy
*rectilinear*G-street; the length*of*its path is at most 9 times the length*of*the shortest path in the L 1 metric, and 9.06 times ... We consider the problem*of*a robot which has to find a target in an unknown simple*polygon*, based only on what it has seen so far. ... Other interesting geometric applications for*competitive*strategies are e. g. the search for the kernel*of*a*polygon*[15, 24, 28, 22] ,*exploration*or path planning in unknown environments [7, 11, 12 ...##
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Competitive searching in a generalized street

1994
*
Proceedings of the tenth annual symposium on Computational geometry - SCG '94
*

We present an on-line strategy for a robot to find the target in an unknown

doi:10.1145/177424.177622
dblp:conf/compgeom/DattaI94
fatcat:xqspvtsb55agrckbmk47t6uqjy
*rectilinear*G-street; the length*of*its path is at most 9 times the length*of*the shortest path in the L 1 metric, and 9.06 times ... We consider the problem*of*a robot which has to find a target in an unknown simple*polygon*, based only on what it has seen so far. ... Other interesting geometric applications for*competitive*strategies are e. g. the search for the kernel*of*a*polygon*[15, 24, 28, 22] ,*exploration*or path planning in unknown environments [7, 11, 12 ...##
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Competitive Online Approximation of the Optimal Search Ratio
[chapter]

2004
*
Lecture Notes in Computer Science
*

We answer these questions for simple

doi:10.1007/978-3-540-30140-0_31
fatcat:hmcx46y6qrhlbisxmgahbbv25u
*polygons*and for undirected graphs, by providing online search strategies that are as good as the best offline search algorithms, up to a constant factor. ... There is also a polynomial time 8-search-*competitive*offline search algorithm. Proof. For a*rectilinear*simple*polygon*, P , Papadimitriou et al. ... Even for*rectilinear*simple*polygons*no polynomial time algorithm for the optimal search path is known, but we can find better online algorithms: Theorem 13 For an agent with vision in a simple*rectilinear*...##
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Competitive Online Approximation of the Optimal Search Ratio

2008
*
SIAM journal on computing (Print)
*

We answer these questions for simple

doi:10.1137/060662204
fatcat:46hnlkwgzne3lc4ertgvipx6ji
*polygons*and for undirected graphs, by providing online search strategies that are as good as the best offline search algorithms, up to a constant factor. ... There is also a polynomial time 8-search-*competitive*offline search algorithm. Proof. For a*rectilinear*simple*polygon*, P , Papadimitriou et al. ... Even for*rectilinear*simple*polygons*no polynomial time algorithm for the optimal search path is known, but we can find better online algorithms: Theorem 13 For an agent with vision in a simple*rectilinear*...##
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Page 2079 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

Hans-Dietrich Hecker (Jena)
2003¢:68234 68U05 68T40 Hammar, Mikael (I-SLRN-IA2; Baronissi); Nilsson, Bengt J.; Schuierer, Sven (D-FRBG-I; Freiburg) Improved

*exploration**of**rectilinear**polygons*. ... The following problem is considered: Given a*rectilinear**polygon*, a point-sized robot has to construct a map*of*it without a priori knowledge*of*the environment. ...##
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Walking in Streets with Minimal Sensing
[chapter]

2013
*
Lecture Notes in Computer Science
*

We also consider a special case

doi:10.1007/978-3-319-03780-6_32
fatcat:7bjlzeclofeo5pgsm3ptr7v6dm
*of*the problem in which the street is*rectilinear*and the search path has to be*rectilinear*. ... We offer a data structure similar to Gap Navigation Tree to maintain the essential sensed data*of*the*explored*street. ... Introducing more general classes*of**polygons*which admit a*competitive*searching with a minimal sensing model is an interesting open problem. ...##
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Page 2381 of Mathematical Reviews Vol. , Issue 95d
[page]

1995
*
Mathematical Reviews
*

For the problem

*of**exploring*a simple*rectilinear**polygon*(under the L; norm), Deng, Kameda, and Papadimitriou gave a 2-*competitive*deterministic algorithm; we present a randomized*exploration*al- gorithm ... Summary: “We consider a number*of*search and*exploration*prob- lems from the perspective*of*robot navigation in a simple*polygon*. ...
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